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arXiv · 1804.07988

Cosheaves

Andrei V. Prasolov
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Abstract

The categories pCS(X,Pro(k)) of precosheaves and CS(X,Pro(k)) of cosheaves on a small Grothendieck site X, with values in the category Pro(k) of pro-k-modules, are constructed. It is proved that pCS(X,Pro(k)) satisfies the AB4 and AB5* axioms, while CS(X,Pro(k)) satisfies AB3 and AB5*. Homology theories for cosheaves and precosheaves, based on quasi-projective resolutions, are constructed and investigated.

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Andrei V. Prasolov. 2018-04-21. Cosheaves. https://arxiv.org/abs/1804.07988

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